liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
St-Petersburg University .
2009 (English)In: Vestnik St. Petersburg University: Mathematics, ISSN 1063-4541, Vol. 49, no 2, 120-129 p.Article in journal (Refereed) Published
Abstract [en]

The problem of finding a solution of the Dirichlet problem for the Laplace equation in the form of a simple layer potential Vρ with unknown density ρ is known to be reducible to a boundary integral equation of the kind Vρ = f to solve for the density, where f are boundary Dirichlet data. It is shown that if S is the boundary of an n-dimensional domain (n > 2) with an outward peak on S, then the operator V −1, which acts on the smooth functions on S, admits a unique extension to an isomorphism between the spaces of traces on S of functions with finite Dirichlet integral over R n and the dual space. Thereby the equation V ρ = f is uniquely solvable for the density ρ for every trace f = u| S of function u with finite Dirichlet integral over R n . Using an explicit description of the space of the traces specified, we can enunciate the theorem on solvability of a boundary integral equation V ρ = f in terms of the function describing the peak cusp.

Place, publisher, year, edition, pages
2009. Vol. 49, no 2, 120-129 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-52019DOI: 10.3103/S1063454109020083OAI: oai:DiVA.org:liu-52019DiVA: diva2:278838
Available from: 2009-11-30 Created: 2009-11-30 Last updated: 2009-12-11

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Maz'ya, Vladimir

Search in DiVA

By author/editor
Maz'ya, Vladimir
By organisation
Department of MathematicsThe Institute of Technology
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 47 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf